2015/04/07 by Sazi Li, Wei Li, Li, Sazi +3
Mathematics · Physics and Astronomy · #Combinatorics #Complex Network Analysis Techniques #Degenerate energy levels #Dimer #Eigenvalues and eigenvectors #FOS: Physical sciences #Ising model #Mathematics #Partition function (quantum field theory) #Phase (matter) #Phase diagram #Phase transition #Physics #Quantum #Quantum many-body systems #Quantum mechanics #Square lattice #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #Topological order #Topology (electrical circuits) #Transfer matrix #cond-mat.stat-mech #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.1504.01566
6 pages, 8 figures, supplementary materials added
openalex publication_date 2015/04/07 · arxiv created 2015/04/08 · arxiv updated 2015/04/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
In this work, we investigate the classical loop models doped with monomers and dimers on a square lattice, whose partition function can be expressed as a tensor network (TN). In the thermodynamic limit, we use the boundary matrix product state technique to contract the partition function TN, and determine the thermodynamic properties with high accuracy. In this monomer-dimer-loop model, we find a second-order phase transition between a trivial monomer-condensation and a loop-condensation (LC) phases, which can not be distinguished by any local order parameter, while nevertheless the two phases have distinct topological properties. In the LC phase, we find two degenerate dominating eigenvalues in the transfer-matrix spectrum, as well as a non-vanishing (nonlocal) string order parameter, both of which identify the topological ergodicity breaking in the LC phase and can serve as the order parameter for detecting the phase transitions.